Scattering of Microwaves from a Cylindrical Plasma in the Born Approximation. I

The scattering of a plane microwave incident upon a cylindrically symmetric non-uniform plasma is treated in the Born approximation. When the electric vector is parallel to the axis of the cylinder, the angular distribution function of the cylindrical wave scattered from a cylindrical collisionless plasma is given by {aligned} f(θ){=}√π/2e(3/4)π j{∫}₀∞k²η(ρ')J₀(2kρ'sinθ/2)ρ'dρ'. {aligned} Here θ is the scattering angle, η=(ω p /ω) 2 with the plasma frequency ω p , and the incident wave is assumed to be proportional to e j (ω t - k x ) . The angular distributions for other cases, e.g. waves with the electric vector perpendicular to the axis and/or plasmas with collision loss in a magnetic field, are simply related to f (θ). For some special density distributions such as that of J 0 -type, the integration in f (θ) can be performed analytically. Finally the same formulas are rederived by summing the radiations from electrons which are forced to oscillate by the incident wave.